On distribution of Grubbs’ statistics in case of normal sample with outlier
- 27 Downloads
We investigate one-sided Grubbs’ statistics for a normal sample. Those statistics are standardized maximum and standardized minimum, i.e., studentized extreme deviation statistics. We consider the case of the sample when there is one abnormal observation (outlier), unknown to what number according. The outlier differs from other observations in values of population mean and dispersion. We obtain recursive relationships for the marginal distribution function of one-sided Grubbs’ statistics. We find asymptotic formulas for marginal distribution functions. We obtain recursive relationships for the joint distribution function of one-sided Grubbs’ statistics and investigate its properties.
Keywordsone-sided Grubbs’ statistics standardized minimum and maximum outlier normal distribution marginal distribution functions asymptotic decompositions joint distribution function power functions for Grubbs’ criteria
Unable to display preview. Download preview PDF.
- 4.Lemeshko, B. Yu. and Lemeshko, S. B. “Extension of Application Domain of Grubbs’ Type Criteria, Using with Rejection of Outlying Observations”, Izmeritel’naya Tekhnika, No. 6, 13–19 (2005) [in Russian].Google Scholar
- 5.Verma, S. P. and Quiroz-Ruiz, A. “Critical Values for 22 Discordancy Test Variants for Outliers in Normal Samples up to Sizes 100, and Applications in Science and Engineering”, Revista Mexicana de Ciencias Geologicas 23, No. 3, 302–319 (2006).Google Scholar
- 8.Fergusson, T. S. “On the Rejection of Outliers”, in Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1, 253–287 (University of California Press, Berkeley, 1961).Google Scholar
- 17.Kalitkin, N. N. Numeric Methods (Nauka, Moscow, 1978) [in Russian].Google Scholar